COVID-19 Notes

First some basic assumptions, for which I think the evidence is strong (reference):

1. R0 ~ (2-3) or higher in a permissive environment -- no strong efforts at social distancing, quarantine, etc.

2. Fatality rate: roughly 1 percent of cases, heavily concentrated in older individuals and/or those with pre-existing conditions. Note this assumes a well-functioning health system and resources for the 5% or so of cases that need intensive care. See below.

3. In situations like #1 above, doubling time could be as short as a few days. Number of infections in Italy grew by ~1000x over the month of February -- i.e., 2^10 or 2+ doublings per week!

USA has perhaps ~1M total hospital beds, over half already occupied, and perhaps 50k ICU spaces. For those infected, the distribution of severity is roughly (again, concentration in vulnerable sub-populations):

80 percent mild case
15 percent serious (may require hospitalization)
5 percent ICU

So roughly 1M infected at a given time would overwhelm US health capabilities. We probably have at least ~1000 infected in the country at the moment, so in the absence of serious measures like social distancing (cancellation of sporting events, large meetings, moving to K12 and college distance learning, etc.), we would reach the health system breaking point in about a month. Many other countries, in Europe and elsewhere, are facing a similar situation.

Whether we impose draconian social measures (which would have a strongly negative effect on cafes, restaurants, hotels, airlines, theaters, etc.) or let COVID-19 infect millions of people, we are in for at least a one quarter downturn (recession?) with the possibility of more significant nonlinear events (complete market collapse, systemic failures). Traders already understand this, which is why equities are in huge decline despite a 50 bp Fed rate cut last week. I went largely to cash already...

We have technology that could help us fight the epidemic. The article below, in the Journal of the American Medical Association, describes how Taiwan successfully handled the epidemic -- less than 50 cases! -- despite close proximity and extensive travel to China. (Note, Taiwan in Jan-Feb is a bit warmer than Milan, but I don't think climate is the entire reason for their good performance...) Google and Apple have these technical (geolocation, tracking) capabilities, but they don't like to emphasize it to the public.

Response to COVID-19 in Taiwan: Big Data Analytics, New Technology, and Proactive Testing

JAMA. Published online March 3, 2020. doi:10.1001/jama.2020.3151

Taiwan is 81 miles off the coast of mainland China and was expected to have the second highest number of cases of coronavirus disease 2019 (COVID-19) due to its proximity to and number of flights between China.1 The country has 23 million citizens of which 850 000 reside in and 404 000 work in China.2,3 In 2019, 2.71 million visitors from the mainland traveled to Taiwan.4 As such, Taiwan has been on constant alert and ready to act on epidemics arising from China ever since the severe acute respiratory syndrome (SARS) epidemic in 2003. Given the continual spread of COVID-19 around the world, understanding the action items that were implemented quickly in Taiwan and assessing the effectiveness of these actions in preventing a large-scale epidemic may be instructive for other countries.

COVID-19 occurred just before the Lunar New Year during which time millions of Chinese and Taiwanese were expected to travel for the holidays. Taiwan quickly mobilized and instituted specific approaches for case identification, containment, and resource allocation to protect the public health. Taiwan leveraged its national health insurance database and integrated it with its immigration and customs database to begin the creation of big data for analytics; it generated real-time alerts during a clinical visit based on travel history and clinical symptoms to aid case identification. It also used new technology, including QR code scanning and online reporting of travel history and health symptoms to classify travelers’ infectious risks based on flight origin and travel history in the past 14 days. Persons with low risk (no travel to level 3 alert areas) were sent a health declaration border pass via SMS (short message service) messaging to their phones for faster immigration clearance; those with higher risk (recent travel to level 3 alert areas) were quarantined at home and tracked through their mobile phone to ensure that they remained at home during the incubation period.

Google + Apple + cell carriers have the data to detect near collisions (proximity) between COVID-19 spreaders (once diagnosed) and other individuals. This can be done anonymously: i.e., public health services get a warning that a spreader visited nursing home X on timestamp T without naming the spreader. Another alternative (see WSJ video below) is to have an OPT-IN app that checks location history and warns if you were in close proximity to a spreader. The PRC government version of this app has been used by 200M+ Chinese already -- note it's OPT-IN. The companies above have the data to do this but don't like it to be known that they can.




Note Added: Latest results from the beginnings of broader testing in Seattle suggest that the virus is widespread in the community already. The number of cases detected is primarily limited by number of tests:

Nature: “We are past the point of containment,” says Helen Chu, an infectious-disease specialist at the University of Washington School of Medicine (UW Medicine) in Seattle. “So now we need to keep the people who are vulnerable from getting sick.”

I checked the weather records for Seattle in February 2020: daily highs in the mid-40s to mid-50s. There is very little chance that wintry areas of the US will be warmer than this over the next 30 days, even with an early spring. So I don't see that US spread in those regions can be mitigated by anything less than social distancing and other strong measures. Weather will probably not save us.

Front line tweets from Italian doctors describe medical resources pushed to the breaking point. I hope we do not experience this in the US, but I don't see how we will avoid it: [1] [2]

Some interesting information about transmission (surfaces, air in confined spaces) at the beginning; Italian overload at 17m; S. Korean data at 19m.

COVID-19: CBA, CFR, Open Borders

Some observations related to COVID-19.

1. Cost-Benefit Analysis: I don't favor this kind of purely economic analysis when human lives are at stake, but at the crudest level we are talking about US policy choices (i.e., lockdown vs permissive sweep) that could lead to of order a million more or fewer deaths. EPA sometimes values a human life at ~$7M, which suggests that the last 10-20 years of life for an older person could be valued at ~$1M. Under these assumptions the economic value of a lockdown which saves a million lives is in the trillion dollar range. This is similar to the cost of shutting down big chunks of the economy for months. So a CBA could go either way depending on detailed assumptions.

2. Open Borders: Many areas of the world are likely to develop into reservoirs for COVID-19. When the US emerges from lockdown it will be in our interests to carefully test (and potentially quarantine) everyone entering the country. I believe Singapore already has such a regime in place, with a reported 3 hour turn around for test results at the airport!

How can we possibly exit lockdown without the kind of control that Singapore exerts? In the COVID-19 reality it is crazy for the US not to impose strict control over the southern border. This will impact the presidential campaign in interesting ways. I don't think it will be tenable for a candidate to tell the virus-weary citizenry that it is impossible to control entry into the country. Once the infrastructure is built to effectively control our borders, it will be difficult to dismantle.

3. Case Fatality Rate: What is the lower bound on CFR (or more precisely, IFR = Infected Fatality Rate)? I have been working under the assumption that about 1% of infected individuals will die from COVID-19, assuming access to good medical care. (IIRC the value from S. Korea data is just below 1%.) I think there is a factor of 2-3 uncertainty in this number, so it could be as low as 0.5 or even 0.3%. Lower numbers are typically justified by invoking many asymptomatic, undetected cases in the population. However, large numbers of undetected infections also imply very rapid spread of the disease.

Rapid spread (e.g., in the absence of a rigorous lockdown) would lead to an overloaded medical system, with a resulting IFR which could be several times higher than the value that applies under good conditions -- so 0.3% could become 1%. In a scenario in which the virus sweeps through most of the population in a relatively short time (e.g., 3-6 months), an overall death rate of 1% times, e.g., 50-70% of the population is still a reasonable estimate. For the USA this would be at least 1.5 million people.

Related posts on COVID-19.

Hospitals in NYC already under stress: WSJ , NYT


Note Added: I've yet to see any detailed calculations for an alternative plan which tries to isolate the most vulnerable while allowing the economy to continue to function. Could it work?

1. Define the vulnerable population: e.g., people over 65 or with pre-existing conditions. Let's say this is 15% of the total population.

2. Try to isolate these people as much as possible. Give them free accommodation in the now empty hotels and college dormitories, on military bases and in makeshift shelters. Guarantee them free food delivery and regular medical checkups in these new locations. Within these locations practice very good internal isolation, as on the Princess cruise ship: isolate each person in their room, require the wearing of (inexpensive; not N95) masks when they emerge for activities, etc. Use the National Guard and military to execute the strategy.

Alternatively, we could leave the vulnerable population in place where they are now and move out any younger people (e.g., family members) they live with into temporary housing, or even confine the younger people in place if they consent to isolation in order to help their elders. The shelter in place order only applies to 65+ instead of the whole population!

It seems that this could be less expensive than the lockdown currently in place.

Uber and Lyft drivers wearing gloves and masks, spraying down their cars periodically, could be used as people movers or for food delivery. Instead of shutting down restaurants, the government could employ them to produce the meals for the sequestered people... The government just has to pay Uber and Lyft through their existing platform. Beats mailing checks to the entire population!

Jeffrey Sachs: Lessons from the COVID Commission, Lab Leak Questions, and Nord Stream — Manifold Episode 21

 

Jeffrey D. Sachs is a world-renowned economics professor, bestselling author, innovative educator, and global leader in sustainable development. Professor Sachs serves as the Director of the Center for Sustainable Development at Columbia University and is a University Professor, Columbia's highest academic rank. 

 

Steve and Jeffrey discuss: 

0:00 Jeffrey Sachs’ experience on the Lancet Commission for COVID-19 

13:41 Potential for bioweapons research 

19:06 Why a lab leak is plausible 

32:38 Possible defenses for COVID coverup 

43:56 Government secrecy and other areas of concern 

48:08 Reflections on Nord Stream sabotage 

Resources: 

The Lancet Commission on lessons for the future from the COVID-19 pandemic, Sachs et al., Sept. 14 2022 

https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(22)01585-9/fulltext 

Why the Chair of the Lancet’s COVID-19 Commission Thinks The US Government Is Preventing a Real Investigation Into the Pandemic, Current Affairs, Aug 3 2022

https://www.jeffsachs.org/interviewsandmedia/64rtmykxdl56ehbjwy37m5hfahwnm5 

Podcast audio. Transcript.

My brief summary:

Sachs led a 2 year study of COVID-19 organized for the Lancet. One of the task forces was focused on COVID-19 origins. Sachs feels that members of this task force were engaged in a deliberate cover up which tried to push the natural origin hypothesis from the beginning. His conclusion is that a lab origin hypothesis is still viable, and indeed more likely than the natural origin hypothesis. 

The US is treaty bound to only do "defensive" bioweapons research and development, but this includes the creation and study of dangerous viral strains -- e.g., so that vaccine efficacy and related technologies can be studied. As far as I can tell the US spends ~$10 billion per annum on biodefense research, much of it funneled through NIAID (NIH institute for infectious diseases). Many of the researchers involved in "gain of function" genetic engineering are funded via NIAID and have been for decades. Sachs claims that the genetic engineering research to add a human-specific cleavage site to a coronavirus was actually performed, although the specific 2017 DEFUSE research plan (uncovered in 2021 investigation) was not funded. 

https://theintercept.com/2021/09/23/coronavirus-research-grant-darpa/

https://www.documentcloud.org/documents/21066966-defuse-proposal

COVID-19: the weeks ahead

The figures below (#deaths) are from the Financial Times (data updates frequently). It's useful to compare NY and US numbers to Lombardia and Italy. In the former case we can extrapolate the slope on the log plot for another week or so, because lockdowns here are recent and death generally happens +2-3wks after infection. For Lombardia / Italy we can start to see some bending of the curve from lockdowns that started about 20 days ago.

Based on these simple observations, I think NY will be ~10k in a week, US perhaps double that. Comparing with the Italian curves, US would be lucky not to reach ~100k by end of April -- i.e. 4 or 5 doublings in next 4 wks, or 2.5k x (16-32) = 40-80k.

In COVID-19 Notes (March 8) I gave my best estimates for key parameters characterizing the epidemic:

1. R0 ~ (2-3) or higher in a permissive environment -- no strong efforts at social distancing, quarantine, etc.

2. Fatality rate: roughly 1 percent of cases, heavily concentrated in older individuals and/or those with pre-existing conditions. Note this assumes a well-functioning health system and resources for the 5% or so of cases that need intensive care. See below.

3. In situations like #1 above, doubling time could be as short as a few days. Number of infections in Italy grew by ~1000x over the month of February -- i.e., 2^10 or 2+ doublings per week!

80 percent mild case
15 percent serious (may require hospitalization)
5 percent ICU

I think these numbers will turn out to be roughly correct. For the cognoscenti: German CFR numbers have been steadily increasing, just under 1% now, SK increasing to about 1.5%. Diamond Princess deaths have reached 10, perhaps more to come.

This is from a widely-circulated post by a New Orleans ER doc:

I am an ER MD in New Orleans. Class of 98 [Texas A&M]. Every one of my colleagues have now seen several hundred Covid 19 patients and this is what I think I know.

Clinical course is predictable.
2-11 days after exposure (day 5 on average) flu like symptoms start. Common are fever, headache, dry cough, myalgias(back pain), nausea without vomiting, abdominal discomfort with some diarrhea, loss of smell, anorexia, fatigue.

Day 5 of symptoms- increased SOB, and bilateral viral pneumonia from direct viral damage to lung parenchyma.

Day 10- Cytokine storm leading to acute ARDS and multiorgan failure. You can literally watch it happen in a matter of hours.

[ NOTE: (2-11) + 10 = 2-3 wks after infection ]

81% mild symptoms, 14% severe symptoms requiring hospitalization, 5% critical.

... Our main teaching hospital repurposed space to open 50 new Covid 19 ICU beds this past Sunday so these numbers are with significant decompression. Today those 50 beds are full. They are opening 30 more by Friday. But even with the "lockdown", our AI models are expecting a 200-400% increase in covid 19 patients by 4/4/2020.

... Everyone is scared; patients and employees. But we are the leaders of that emergency room. Be nice to your nurses and staff. Show by example how to tackle this crisis head on. Good luck to us all.

Judging from the video below, I would guess that there are at least ~1 million people in NYC among whom the infection rate has been rapid (~3 day doubling timescale) for a long time, with little to no reduction due to the lockdown. If this is correct, we can expect a huge number of deaths and critical cases from this population alone -- perhaps 10k deaths, 50k critical cases.




Added: This is an interview with one of the leading CV-19 experts in Korea. Not much new for readers of this blog, but a good introduction for the general population. Perhaps most interesting: discussion of masks at @15m (droplet and aerosol transmission just before that), followed by the Korean approach to the epidemic. Alarmingly, @8m he describes known cases of individual re-infection after recovery!

COVID-19: CFR ~1% estimated in large random sample (Austria)

CV19 antigen test of a random representative sample in Austria. CFR (or IFR, to be very precise) is close to 1%.

WSJ: More twice as many people have been infected by the new coronavirus in Austria than official figures showed, according to a new survey, with a fatality rate of 0.77%.

The nationwide survey, which the Austrian government described as the first of a country with a sizable population, showed that lockdown measures, which are particularly strict in Austria, were necessary to avoid mass casualties and overwhelming the health-care system, said Heinz Fassmann, the country’s education minister, who presented the study in Vienna Friday.

The study, conducted by polling firm SORA in cooperation with the government the Red Cross, tested a random, representative sample of 1,544 people aged 0 to 94 from across the country in their homes or in drive-in testing stations. It indicated that 28,500 people, or around 0.33% of Austria’s 8.9 million population, were infected with the virus by April 6, sharply higher than the 12,467 infections recorded by that date, with 220 people dying of Covid-19, the disease the virus causes.

The findings suggest that while the death rate implied from the study, 0.77%, is lower than the World Health Organization’s estimate for reported cases, which is over 3%, it would still mean that the virus could kill many millions of people before a vaccine is available.

95% confidence interval for infection rate is 0.12% to 0.76%, so CFR range of ~0.3% to ~2%. The "standard model" of CV-19 epidemiology seems to be correct.

Note Added: First sign of Google / Apple action to bring the full power of geolocation to bear on contact tracing and isolation! These capabilities have been available in China for some time now.

Bloomberg: Apple Inc. and Google unveiled a rare partnership to add technology to their smartphone platforms that will alert users if they have come into contact with a person with Covid-19. People must opt in to the system, but it has the potential to monitor about a third of the world’s population.

The technology, known as contact-tracing, is designed to curb the spread of the novel coronavirus by telling users they should quarantine or isolate themselves after contact with an infected individual.

The Silicon Valley rivals said on Friday that they are building the technology into their iOS and Android operating systems in two steps. In mid-May, the companies will add the ability for iPhones and Android phones to wirelessly exchange anonymous information via apps run by public health authorities. The companies will also release frameworks for public health apps to manage the functionality.

This means that if a user tests positive for Covid-19, and adds that data to their public health app, users who they came into close proximity with over the previous several days will be notified of their contact. This period could be 14 days, but health agencies can set the time range.

The second step takes longer. In the coming months, both companies will add the technology directly into their operating systems so this contact-tracing software works without having to download an app. Users must opt in, but this approach means many more people can be included. Apple’s iOS and Google’s Android have about 3 billion users between them, over a third of the world’s population. ...

COVID-19: Exiting Lockdown and Geolocation

Pressure will mount around the end of this month (assuming we are past the peak death rate and virus spread is under control) for the US to exit lockdown. This needs to be done in a smart way, which includes:

1. Required use of facemasks
2. Cocooning of vulnerable populations
3. Contact tracing and forced isolation of cases, perhaps using geolocation technology

See related posts

COVID-19: Smart Technologies and Exit from Lockdown (Singapore)
COVID-19: CBA, CFR, Open Borders
COVID-19: Cocoon the vulnerable, save the economy?
COVID-19 Notes

WSJ: Western governments aiming to relax restrictions on movement are turning to unprecedented surveillance to track people infected with the new coronavirus and identify those with whom they have been in contact.

Governments in China, Singapore, Israel and South Korea that are already using such data credit the practice with helping slow the spread of the virus. The U.S. and European nations, which have often been more protective of citizens’ data than those countries, are now looking at a similar approach, using apps and cellphone data.

“I think that everything is gravitating towards proximity tracking,” said Chris Boos, a member of Pan-European Privacy-Preserving Proximity Tracing, a project that is working to create a shared system that could take uploads from apps in different countries. “If somebody gets sick, we know who could be infected, and instead of quarantining millions, we’re quarantining 10.” ...

Some European countries are going further, creating programs to help track individuals—with their permission—who have been exposed and must be quarantined. The Czech Republic and Iceland have introduced such programs and larger countries including the U.K., Germany and Spain are studying similar efforts. Hundreds of new location-tracking apps are being developed and pitched to those governments, Mr. Boos said.

U.S. authorities are able to glean data on broad population movements from the mobile-marketing industry, which has geographic data points on hundreds of millions of U.S. mobile devices, mainly taken from apps that users have installed on their phones.

Europe’s leap to collecting personal data marks a shift for the continent, where companies face more legal restrictions on what data they may collect. Authorities say they have found workarounds that don’t violate the European Union’s General Data Protection Regulation, or GDPR, which restricts how personal information can be shared. ...

Google, Apple, Facebook, etc. are reluctant to draw attention to their already formidable geolocation capabilites. But this crisis may focus public awareness on their ability to track almost all Americans throughout the day.

WSJ: Google will help public health officials use its vast storage of data to track people’s movements amid the coronavirus pandemic, in what the company called an effort to assist in “unprecedented times.”

The initiative, announced by the company late Thursday, uses a portion of the information that the search giant has collected on users, including through Google Maps, to create reports on the degree to which locales are abiding by social-distancing measures. The “mobility reports” will be posted publicly and show, for instance, whether particular localities, states or countries are seeing more or less people flow into shops, grocery stores, pharmacies and parks. ... 

This is just a hint at what Google is capable of. Check out Google Timeline! Of course, users have to opt in to create their Google Timeline. But it should be immediately obvious that Google already HAS the information necessary to populate a detailed geolocation history of every individual...




Added from the comments:

There are really two separate issues here:

1. What is the basic epidemiology of CV19? i.e., R0, CFR, age distribution of vulnerability, comorbidities, mechanism of spread, utility of masks, etc.

2. What is the cost benefit analysis for various strategies (e.g., lockdown vs permissive sweep with cocooning)

While we have not reached full convergence on #1 I think reasonable people agree that the "mainstream" consensus has a decent chance of being correct: e.g., CFR ~ 1% or so, possibility of wide sweep in any population, overload of ICUs means much higher CFR, warmer weather might not save the day, etc. Once this scenario for #1 has, say, >50% chance of being right you are forced to at least take it seriously and then you are on to #2. (It is not required to believe that the scenario above is true at 95% or 99% confidence level...)

#2 is a question of trade-offs and two reasonable people can easily disagree until the end of time... I've already posted very simple CBA that show the answer can go either way depending on how you "price" QALYs, what you think long term effects on economy are from lockdown -- i.e., how fragile you think financial, supply chain, psychological systems are in various places; is it a ~$trillion cost, or could it go nonlinear?

Re: Physicists (and addressing gmachine comment below which has a lot of truth in it), we have no trouble understanding modeling done by other people (whether in finance, climate, or epidemiology), and we are also trained to deal with very uncertain data / statistical situations. We can "take apart" the model in our head to see where the dependencies are and how the uncertainties propagate through the model. I am amazed often to meet people who built a very complex model (e.g., thousands of lines of code, lots of input parameters), but they lack the chops to develop good intuition for how their model works, to make qualitative estimates for uncertainty quantification, etc. I have seen this in economics, finance, biology, and climate contexts many times. "There are levels to this thing..." Understanding the model can be more g-loaded than building it!

Finally, we are trained to think from first principles -- which assumptions are crucial to reach the conclusions, which are not? What are the key uncertainties in the analysis? Do we really need very specific assumptions about, e.g., social interaction rates as in the Imperial models? Or can I do a quick Fermi estimate which gets me a more robust answer at the cost of a factor of 2 uncertainty that does not really affect the main conclusion -- e.g., will ICU overload happen?

Enrico Fermi at the Trinity test: "I tried to estimate its strength by dropping from about six feet small pieces of paper before, during, and after the passage of the blast wave. Since, at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2 1/2 meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T." The actual yield was about 20 kt. Sometimes a smart guy can get to within a factor of two, and with much greater clarity, than a huge team of modelers...

COVID-19 Update: Developing Countries and Flattening the US Curve

SITUATION IN THE PHILIPPINES:

One of the key unknowns about this epidemic is the status of developing countries, for example those in warm equatorial regions such as in Africa and India. If we are fortunate, we will find that warm weather and humidity inhibit the spread of COVID-19. But this is not yet conclusively established.

In the video below Dr. John Campbell describes the situation in the Philippines (population 100M): hospitals are overwhelmed in Manila (population 20M) and drastic measures have been taken by the government. Given the lack of medical infrastructure, the mortality rate there could be well above 1% for cases. This would mean millions of deaths if the virus sweeps the population.

Even worse, we might expect the epidemic to play out similarly among billions of other people around the world. Perhaps climactic protection does not extend to Manila for specific reasons, such as the widespread use of air conditioning, the large malls and food courts, etc. (What is happening in Bangkok and Kuala Lumpur?) Or perhaps Manila is a harbinger of what is to come in many other countries.

The Philippines case study might give important clues as to the seasonality of COVID-19. How much relief will summer provide?





FLATTENING THE CURVE IN THE US:

The calculations below are from an email I sent yesterday, describing what is required to "flatten the curve" in the US. The dotted line in the figure above can be interpreted as roughly 0.3 percent infected in any local population region (e.g., NYC or Seattle). For the US as a whole, this is ~1 million total infections in the country at any given time.

By my estimates the US health system will be overwhelmed if we have to deal with ~1 million cases (which is only 0.3% of the population) at any instant of time. This comes from counting free ICU space (~50k beds in US) and the observed fact that ~5% of cases require intensive care. See more here:

https://infoproc.blogspot.com/2020/03/covid-19-notes.html

If the number of infected at any given time is higher than ~1M the mortality rate will be higher than the ~1% observed under good medical conditions. Even under good conditions, where the 1% applies: 50% of US population infected (i.e., some kind of sweep) means 1.5 million deaths! This could easily be 2 or 3 times higher if our health system is overwhelmed, as in northern Italy and Iran.

Now, assuming an ICU treatment period of 7 days (optimistic?), the amount of time required to deal with 1 million infected at a time on the way to an integrated 150 million (i.e., 50% infected) is 7 x 150 days = 150 weeks... about 3 years! Obviously during this period we would build more intensive care infrastructure, etc. but the point remains that flattening the curve so that we avoid the situation where people who need intensive care are turned away, causing death rate among cases to shoot well above 1%, will be challenging!

I think aggressive measures are absolutely necessary to avoid a catastrophic outcome. Whether, e.g., K-12 closures have a material impact on that is not completely clear to me, but I think we should probably err on the side of caution.

We have to reduce R0 drastically before hitting ~1M cases or we are in for mass panic. In February Italian cases grew by 1000x. That means we have only weeks to get things under control in US before we overwhelm our health system.

The main unknown: How effective are the measures now widely taken in the US (schools and companies moving to remote operation, expanded testing and quarantine) going to be in reducing the doubling rate from 2+ times per week (i.e., doubling time of few days, as observed in Italy in February) to something less rapid?

We are going to find out in coming weeks.

COVID-19, Blockchain, and the Global Startup Scene - Manifold Podcast #39

Steve and Corey talk to Kieren James-Lubin and Victor Wong of the blockchain technology startup, BlockApps. They begin with a discussion of the COVID-19 epidemic (~25m): lockdown, predictions of ICU overload, and helicopter money. Will personal contact tracking become the new normal? Transitioning to blockchain, a technology many view as viable even in times of widespread societal disruption, they give a basic explanation of the underlying cryptographic and consensus algorithms. Kieren and Victor explain how BlockApps was founded, its business model, and history as a startup. They conclude with a comparison of startup ecosystems in China, Silicon Valley, and NYC.

Recorded on March 18, 2020. Now (March 26) I feel we can make much stronger predictions about CV-19 in the US. We will definitely see overloaded health systems (ICUs) across a broad part of the country. It is already starting to happen in NYC. I will be surprised if the US can avoid tens of thousands of fatalities by early April (say, 14 days from today).

1:08 - Lockdown and ICU Overload COVID-19
5:22 - Singapore and Taiwan Response
17:28 - Government Intervention and Helicopter Money
22:13 - End of the Lockdown?

25:58 - How BlockApps got started
28:56 - Private & Public Key Cryptography and Digital Signatures
34:40 - Blockchain
46:05 - Enterprise Blockchains
1:03:37 - Elevator Pitch
1:24:58 - Global Startup Scene

Transcript

Kieren James-Lubin

Victor Wong


man·i·fold /ˈmanəˌfōld/ many and various.

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Steve Hsu and Corey Washington have been friends for almost 30 years, and between them hold PhDs in Neuroscience, Philosophy, and Theoretical Physics. Join them for wide ranging and unfiltered conversations with leading writers, scientists, technologists, academics, entrepreneurs, investors, and more.

Steve Hsu is VP for Research and Professor of Theoretical Physics at Michigan State University. He is also a researcher in computational genomics and founder of several Silicon Valley startups, ranging from information security to biotech. Educated at Caltech and Berkeley, he was a Harvard Junior Fellow and held faculty positions at Yale and the University of Oregon before joining MSU.

Corey Washington is Director of Analytics in the Office of Research and Innovation at Michigan State University. He was educated at Amherst College and MIT before receiving a PhD in Philosophy from Stanford and a PhD in a Neuroscience from Columbia. He held faculty positions at the University Washington and the University of Maryland. Prior to MSU, Corey worked as a biotech consultant and is founder of a medical diagnostics startup.

COVID-19: CDC US deaths by age group

Reader LondonYoung points to this CDC data set. Table 2 is reproduced below.

If we assume that CV-19 has infected a few percent of the total US population, we should multiply the numbers in the CV-19 deaths column by ~30x to extrapolate to a full population sweep. With that adjustment factor the impact on people younger than 25 is still very modest. It is only among people ~50y or older for whom the effect of a full CV-19 sweep is comparable to All-Cause deaths.

As a rough estimate I'd guess a full population sweep (under good medical conditions) costs about 10M QALYS. How much is that worth? A few trillion dollars?

Of course, we should keep in mind that there might be very negative long-term health consequences from serious cases of CV-19 infection that do not result in death.

Added:

1. Germany’s leading coronavirus expert Christian Drosten on Merkel’s leadership, the UK response, and the ‘prevention paradox’ (Guardian).

2. US National Academy of Sciences COVID-19 Update.

COVID-19: Some US estimates -- the knife's edge

My lower bound on current number of cases in the US (March 18): tens of thousands. Positive test results are just the tip of the iceberg.

The unconstrained doubling time is roughly 3 days. Some recent estimates of this timescale by country (note these are trailing estimates): Japan is ~10 days, S. Korea ~16, PRC ~36 days currently. Most European countries are at 3-4 days, although these estimates are unreliable as the increase is mainly due to wider testing and does not capture growth rate very well.

In Michigan we've closed K-12 schools and universities, as well as bars, restaurants, gyms, etc. I would guess that the doubling time has been increased to ~7 or 10 days by these measures.

Medical system overload will happen for sure at ~1 million total cases in the US, based on 5% of cases requiring intensive care, and total ICU capacity (~50k) in the US. Local regions may go into crisis much earlier, in particular dense urban regions that are more cosmopolitan than the US as a whole. The threshold is roughly 0.3 percent of population infected -- only a few per thousand!

Overload may happen much earlier -- hospital systems run at over 90% occupancy. So most spaces are already filled by sick people. The numbers above might be optimistic by an order of magnitude -- perhaps 100k total cases in US, or 0.03 percent of local population infected will lead to at least some health system crises.

Another factor contributing to early overload is exhaustion of protective equipment for medical personnel (already starting to happen in some places like WA) and eventual sickness of those personnel.

Best case: Widespread US crisis after another (3-5) doublings:  2^3 to 2^5 more cases. Assuming the whole country adopts isolation measures as in Michigan: roughly 30 days until widespread crises. I suspect we will see localized crises much sooner.

How might things turn out better?

Warm weather plus isolation measures push doubling time to 14 or even 20 days. Even in the best case this won't apply throughout the whole country, so still expect problems in some regions.

Earlier posts: COVID-19 Notes , COVID-19 Update: Developing Countries and Flattening the US Curve.


The figures below are from this NYTimes article describing a Harvard analysis similar to the one above. Note in the first figure the solid yellow line is crossed in all scenarios very early on -- i.e., +1 or 2 months. Overloaded ICUs are likely in the near future.

COVID-19: A False Lockdown Dichotomy?

This was posted by commenter "husposter" in the thread for COVID-19: CBA, CFR, Open Borders, and I thought I would promote it here. Along similar lines, I read somewhere today that economic indicators for Sweden (no lockdown) are quite similar to those for neighboring countries that are under lockdown. Rational people will tend to enact social distancing even if it is not forced on them.

From what I understand, CV-19 is a terrible infection to have even for many people who avoid going to hospital. There may be an ~80% chance of a mild or entirely asymptomatic case, but the tail of the probability distribution is very unpleasant... and in the worst case, it seems like a terrible way to die.

husposter: Why do people assume that the economy will "get back to normal" if the lockdown is ended without the disease being controlled?

Are all you people going to start going to the bar and baseball games if the government lets you? Are you going to let you kids go to what are effectively infection factories (daycares and schools)? Are you going to start going to doctors offices full of people that might have Covid?

The "lockdowns" came AFTER the private market started to shut down voluntarily. I was there. I saw it. My company was canceling travel and the NBA was cancelling its season while "the government" was still encouraging people to go out.

Who the heck is going to take a 1% chance of dying? A 10% chance of hospital stay and permanent lung damage? Who is going to expose friends, loved ones, and co-workers to that chance if they get infected?

To even propose that there is some kind of "choice" to save the economy at the price of a few old people dying (and its not like the victims are even as clear as you'd like it to be) is a dangerous false dichotomy. There is no way the economy is exiting the lockdown until the disease is under control.

The "lockdown" just gives the authorities the ability to go after egregious malcontents that are so socially degenerate they can't obey basic behavioral norms at a time like this. Your workplace would not be open right now even if the government allowed it.

Either get the disease under control, or there is no economy. You aren't a clever heartless individual, you're an idiot that wants to seem "tough".

This is what people would be risking so they could go to a concert:

It first struck me how different it was when I saw my first coronavirus patient go bad. I was like, Holy shit, this is not the flu. Watching this relatively young guy, gasping for air, pink frothy secretions coming out of his tube and out of his mouth. The ventilator should have been doing the work of breathing but he was still gasping for air, moving his mouth, moving his body, struggling.

We had to restrain him. With all the coronavirus patients, we’ve had to restrain them. They really hyperventilate, really struggle to breathe. When you’re in that mindstate of struggling to breathe and delirious with fever, you don’t know when someone is trying to help you, so you’ll try to rip the breathing tube out because you feel it is choking you, but you are drowning.

When someone has an infection, I’m used to seeing the normal colors you’d associate with it: greens and yellows. The coronavirus patients with ARDS have been having a lot of secretions that are actually pink because they’re filled with blood cells that are leaking into their airways. They are essentially drowning in their own blood and fluids because their lungs are so full. So we’re constantly having to suction out the secretions every time we go into their rooms.

Added: WSJ on exiting lockdown in Wuhan... important sociological and public health experiment to watch.




Good twitter thread by J.D. Vance addressing skeptics.

More Added: Ioannidis preprint estimates that a large fraction (e.g., ~30 percent) of US CV19 dead are under 65, in sharp contrast to Europe and Asia (~5 percent). This suggests (as pointed out many times by commenters here) that cocooning may be more difficult here than abroad. While this data is very noisy at the moment it is hard to believe that the entire difference is due to noise.

COVID-19: Smart Technologies and Exit from Lockdown (Singapore)

How will we exit lockdown? Once the rate of spread of COVID-19 has been reduced sufficiently, we should be able to switch to a more precise, targeted methodology. (Of course, widespread testing is a prerequisite baseline capability...) Below are some methods in use in Singapore.



This is the most benign app for contact tracing I can imagine. But it requires a large fraction of people to be running it on their phones. Geo-location capabilities are strong enough that most governments could do this without the opt-in app. They should prepare a legal consent form for future use that permits aggressive contact tracing using all data available (e.g., from Google or Apple or cell carriers). Most people who are diagnosed with CV-19 would probably consent to the use of their geo-location data to help others they may have infected.

Here's a simple system for enforcing home quarantine. If the UK and US governments can't deploy something like this to help us exit from lockdown in a month or two, then our civilization is toast!

The simplest technology of all is to get everyone to wear a mask in public. Not a fancy N95 mask - even a home made paper or cloth mask would do to stop droplet spray. This is likely as effective as social distancing in stopping virus spread. I suspect widespread use of masks may have helped countries like Japan and Taiwan significantly.

People who are bemoaning the economic costs of this lockdown should be very focused on technologies and behaviors that will allow us to exit as soon as possible, while keeping the epidemic under control.

COVID-19: Open Thread

I haven't followed the latest scientific progress very carefully for the last week or two. It seems that things have slowed down a bit. Previous posts on COVID-19.

I still think the evidence is reasonably strong for IFR ~ 1% (meaning could be 0.5% under good conditions, higher if medical systems are overwhelmed; there seems to be some evidence for dosage dependence of severity as well).

I suspect that from a purely utilitarian perspective we might be overpaying per QALY.

Tests seem to be improving (e.g., Roche), and there seems to be positive early news about vaccines.

Does anyone know what the status of contact tracing apps is? Are there any that have been tested at scale outside of E. Asia?

Where and When were the earliest cases? Is there any evidence for functional (rather than simply genomic) differences between strains?

Please add any useful updates in the comments below.

How Dominic Cummings And The Warner Brothers Saved The UK

Photo above shows the white board in the Prime Minister's office which Dominic Cummings and team (including the brothers Marc and Ben Warner) used to convince Boris Johnson to abandon the UK government COVID herd immunity plan and enter lockdown. Date: March 13 2020. 

Only now can the full story be told. In early 2020 the UK government had a COVID herd immunity plan in place that would have resulted in disaster. The scientific experts (SAGE) advising the government strongly supported this plan -- there are public, on the record briefings to this effect. These are people who are not particularly good at order of magnitude estimates and first-principles reasoning. 

Fortunately Dom was advised by the brothers Marc and Ben Warner (both physics PhDs, now working in AI and data science), DeepMind founder Demis Hassabis, Fields Medalist Tim Gowers, and others. In the testimony (see ~23m, ~35m, ~1h02m, ~1h06m in the video below) he describes the rather dramatic events that led to a switch from the original herd immunity plan to a lockdown Plan B. More details in this tweet thread.

See also How Brexit was won, and the unreasonable effectiveness of physicists.

I checked my emails with Dom during February and March, and they confirm his narrative. I wrote the March 9 blog post Covid-19 Notes in part for Dom and his team, and I think it holds up over time. Tim Gowers' document reaches similar conclusions.

 

Seven hours of riveting Dominic Cummings testimony from earlier today. 

Transcript.

Shorter summary video (Channel 4). Summary live-blog from the Guardian.

This is a second white board used in the March 14 meeting with Boris Johnson:

Warren Hatch on Seeing the Future in the Era of COVID-19: Manifold Episode #50

Steve and Corey talk to Warren Hatch, President and CEO of Good Judgment Inc. Warren explains what makes someone a good forecaster and how the ability to integrate and assess information allows cognitively diverse teams to outperform prediction markets. The hosts express skepticism about whether the incentives at work in large organizations would encourage the adoption of approaches that might lead to better forecasts. Warren describes the increasing depth of human-computer collaboration in forecasting. Steve poses the long-standing problem of assessing alpha in finance and Warren suggests that the emerging alpha-brier metric, linking process and outcome, might shed light on the issue. The episode ends with Warren describing Good Judgment’s open invitation to self-identified experts to join a new COVID forecasting platform.

Transcript

Good Judgment Inc.

Good Judgment Open

Superforecasting: The Art and Science of Prediction

Noriel Roubini (Wikipedia)


man·i·fold /ˈmanəˌfōld/ many and various.

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Steve Hsu and Corey Washington have been friends for almost 30 years, and between them hold PhDs in Neuroscience, Philosophy, and Theoretical Physics. Join them for wide ranging and unfiltered conversations with leading writers, scientists, technologists, academics, entrepreneurs, investors, and more.

Steve Hsu is VP for Research and Professor of Theoretical Physics at Michigan State University. He is also a researcher in computational genomics and founder of several Silicon Valley startups, ranging from information security to biotech. Educated at Caltech and Berkeley, he was a Harvard Junior Fellow and held faculty positions at Yale and the University of Oregon before joining MSU.

Corey Washington is Director of Analytics in the Office of Research and Innovation at Michigan State University. He was educated at Amherst College and MIT before receiving a PhD in Philosophy from Stanford and a PhD in a Neuroscience from Columbia. He held faculty positions at the University Washington and the University of Maryland. Prior to MSU, Corey worked as a biotech consultant and is founder of a medical diagnostics startup.

COVID-19: Iceland tests 10% of population, CFR ~0.5%

I can't find a better reference for this than the Daily Mail, which may have garbled the results. But if the headline is correct, CFR ~ 0.4% (this may increase as the disease runs its course among the infected) and infection rate is just over 4% (1.6k infected / 36k tested). [ See update below the graph for better information. ]

Daily Mail: Iceland has tested one-tenth of its population for coronavirus at random and found HALF of people have the disease without realising - with only seven deaths in 1,600 cases

At the JHU coronavirus page, the latest numbers reported are 1700 infected with 8 dead, or CFR ~ 0.47%. From the graph below it appears that most infections in Iceland happened less than 2-3 weeks ago, suggesting that further deaths will result among the population currently infected. See here for comprehensive Iceland data. From the description there, about half the people tested were already in quarantine (e.g., due to contact tracing), so the Daily Mail claim that the results come from random sampling of the population does not seem correct.

If the 1700 positives did result from testing a completely random selection of 1/10 of the total population, then IFR ~ 8 / 17000 ~ 0.04%, which is very small.

But 4% infected (probably less, due to bias in sampling from quarantine) seems inconsistent with a super-rapid sweep, and is far short of herd immunity. [ See below for better information! ]

Added: I found a better source of information than the Daily Mail.

Iceland Review: ... The screenings of the general population have been carried out by Reykjavík-based medical research company deCODE genetics ...

CEO Dr. Kári Stefánsson: “Fifty per cent of those that test positive in our screenings of the general population are symptom-free at the time. Many of them get symptoms later,” Kári said.

Therefore, although about half of those who have tested positive for coronavirus in deCODE’s screenings did not have symptoms at the time, most of those who have tested positive developed symptoms at some point. A positive sample from an individual without symptoms means that the sample was most likely taken early in the virus’ incubation period, before symptoms such as dry cough or fever began to present themselves.

“DeCODE has now screened 10,401 individuals in Iceland. Of those, 92 were positive. So about 0.9% of those who we screened in the general population turned out to be positive. And that is probably the upper limit of the distribution of the virus in society in general,” Kári explained.

Interview: “The testing has been going on for 15 days – there was a little pause in the middle because we were missing swabs – but all of these 15 days, the rate of positives has been a little bit below one percent, which makes it likely that this is the true population prevalence. Today we are calling in people randomly, just selecting at random from the telephone directory. There is probably no perfect way to get a random sample. But I think it is very likely that the number is going to turn out in the end to be somewhat close to this number, probably somewhere between 0.5-1%.”

If the population prevalence of infection now is 0.5 to 1% (or 1.8k to 3.6k people in all of Iceland), then the 8 deaths imply an IFR in the range 0.22% to 0.44%. This should go up over time as many of the infections are early and we expect more deaths later. The 4% infection prevalence obtained using the Daily Mail numbers is probably an overestimate due to testing of already quarantined people -- DeCode has done about half the testing in Iceland, presumably using the random sampling method described by Stefansson, and another entity did the rest. All of this is aggregated in the current ~1.7k total confirmed cases as of now.

DeCode has genetic data on essentially all Icelanders, so should be able to identify alleles that make one more or less vulnerable to CV19.

COVID-19: Cocoon the vulnerable, save the economy?

1. Define a high-risk (age 65+, pre-existing condition) and low-risk population. Perhaps 15% in the first category, 85% in the latter.

2. Let the low-risk people go back to work. Start the economy up again.

3. Issue a "shelter in place" order for ALL high-risk people. Low-risk individuals who co-habit with high-risk people (e.g., family members) have a choice: self-isolate as well, or move into government provided accommodation.

4. The isolated people receive regular food deliveries and medical care (virus tests). Existing platforms for food delivery (Lyft, Uber) can be used almost immediately for this purpose.

This seems to be a good solution in that:

a. it minimizes damage to the economy,
b. reduces deaths significantly (if executed efficiently), and
c. matches the sacrifices (inconveniences) to the people who benefit most.

Would it work? When I first heard about herd immunity and cocooning the vulnerable, I was skeptical. But now that whole countries have experienced lockdown, and financial markets have descended into chaos, I suspect that the solution above would be widely acceptable as an alternative.

Previous discussion of this idea:

I've yet to see any detailed calculations for an alternative plan which tries to isolate the most vulnerable while allowing the economy to continue to function. Could it work?

1. Define the vulnerable population: e.g., people over 65 or with pre-existing conditions. Let's say this is 15% of the total population.

2. Try to isolate these people as much as possible. Give them free accommodation in the now empty hotels and college dormitories, on military bases and in makeshift shelters. Guarantee them free food delivery and regular medical checkups in these new locations. Within these locations practice very good internal isolation, as on the Princess cruise ship: isolate each person in their room, require the wearing of (inexpensive; not N95) masks when they emerge for activities, etc. Use the National Guard and military to execute the strategy.

Alternatively, we could leave the vulnerable population in place where they are now and move out any younger people (e.g., family members) they live with into temporary housing, or even confine the younger people in place if they consent to isolation in order to help their elders. The shelter in place order only applies to 65+ instead of the whole population!

It seems that this could be less expensive than the lockdown currently in place.

Uber and Lyft drivers wearing gloves and masks, spraying down their cars periodically, could be used as people movers or for food delivery. Instead of shutting down restaurants, the government could employ them to produce the meals for the sequestered people... The government just has to pay Uber and Lyft through their existing platform. Beats mailing checks to the entire population!

Diamond Princess data: "3,711 passengers and crew members onboard. Passengers were initially to be held in quarantine for 14 days. However, those that had intense exposure to the confirmed case-patient, such as sharing a cabin, were held in quarantine beyond the initial 14-day window [3]. By 20th February, there were 634 confirmed cases onboard (17%), with 328 of these asymptomatic (asymptomatic cases were either self-assessed or tested positive before symptom onset) [3]. Overall 3,063 PCR tests were performed among passengers and crew members." Among the infected were many younger passengers and crew members, but the 7 individuals who died were all 70+. AFAIK 10-20 more individuals were in critical condition and we don't know their ultimate fate, but clearly the worst outcomes are highly concentrated among older people. This is reflected in the data from Italy, PRC, and S. Korea as well.

Note: as of March 24 the number of deaths has reached 10, but I don't know the age distribution. In recent NYC data it looks like ~80% are over 60 and the rest a bit younger.

COVID-19: False Positive Rates for Serological Tests

It looks like very few of the tests have false positive rates in the percent range. Since most populations (with the exception of NYC and some other highly impacted places) do not have infection rates higher than a few percent, there is a danger of overestimating total infection rates and underestimating IFR using these tests. (See, e.g., the recent Stanford-USC papers.)

Sure Biotech seems to be an HK company, while Wondfo is in Guangzhou.

NYTimes: ... Each test was evaluated with the same set of blood samples: from 80 people known to be infected with the coronavirus, at different points after infection; 108 samples donated before the pandemic; and 52 samples from people who were positive for other viral infections but had tested negative for SARS-CoV-2.

Tests made by Sure Biotech and Wondfo Biotech, along with an in-house Elisa test, produced the fewest false positives.

A test made by Bioperfectus detected antibodies in 100 percent of the infected samples, but only after three weeks of infection. None of the tests did better than 80 percent until that time period, which was longer than expected, Dr. Hsu said.

The lesson is that the tests are less likely to produce false negatives the longer ago the initial infection occurred, he said.

The tests were particularly variable when looking for a transient antibody that comes up soon after infection, called IgM, and more consistent in identifying a subsequent antibody, called IgG, that may signal longer-term immunity.

“You can see that antibody levels rise at different points for every patient,” Dr. Hsu said. The tests performed best when the researchers assessed both types of antibodies together. None of the tests could say whether the presence of these antibodies means a person is protected from reinfection, however.

The results overall are promising, Dr. Marson added. “There are multiple tests that have specificities greater than 95 percent.”

Preprint: Test performance evaluation of SARS-CoV-2 serological assays

From Table 2 in the paper:

Dr. Patrick Hsu -- quoted in the Times article above, and a co-author of the paper -- is no relation, although we know each other. He has appeared in this blog before for his CRISPR work.

COVID-19: NYC and US estimates

NYC analysis: total deaths (red line) are growing at ~10x per week. Because death typically occurs at least +14 days after infection, the behavior of this curve (doubling timescale, or slope of log plot) is mostly baked in for the next two weeks. It depends on the trailing rate of growth of infections, which has not slowed very much, except perhaps in the last week or so.

Only in the last week or less have we seen significant lockdown and isolation in NYC. So I would be very surprised if there were not another factor of 10x growth in total deaths in the next ~10 days. This would mean over a thousand total deaths, and at least roughly five thousand in need of intensive care (i.e., about 5 cases in critical condition for each fatality). This is, I believe, greater than the available ICU capacity in NYC, even including emergency expansion, military hospital ships, etc. (Roughly, 2k base + 1k emergency expansion + 1k hospital ships. Cuomo has talked about this recently.)

With deep sadness, I predict a health system crisis in NYC within a week or so.

The analogous graphs for the US as a whole also have total deaths and total infections growing with a ~3 day doubling timescale. The infection numbers are mainly limited by testing, but there is no reason to expect a significant decrease in slope of the red (deaths) curve. There is probably another 10x growth in total fatalities over the next ~14 days that we can no longer affect -- the infections have already happened.

Figures obtained here.

A week may have been too optimistic...

NYT: ... All of the more than 1,800 intensive care units in the city are expected to be full by Friday, according to a Federal Emergency Management Agency briefing obtained by The New York Times. Patients could stay for weeks, limiting space for newly sickened people.

... At least two city hospitals have filled up their morgues, and city officials anticipated the rest would reach capacity by the end of this week, according to the briefing. The city requested 85 refrigerated trailers from FEMA for mortuary services, along with staff, the briefing said.

... Other doctors said they had tried to resuscitate people while drenched in sweat under their protective gear, face masks fogging up. Some patients have been found dead in their rooms while doctors were busy helping others, they said.

Wuhan Coronavirus

[ See update: COVID-19 Notes or use the search label Epidemics.]

The Wuhan coronavirus outbreak (see WHO resource) caused me to look back at a paper I wrote in 2003 with A. Zee. We were motivated at the time by the recent SARS outbreak. Some results in the paper may be relevant today.

For Wuhan coronovirus the important parameters such as R0 (average number of secondary cases caused by a single infected individual) and lethality are still to be determined.

Global Spread of Infectious Diseases (ArXiv)

S. Hsu, A. Zee

We develop simple models for the global spread of infectious diseases, emphasizing human mobility via air travel and the variation of public health infrastructure from region to region. We derive formulas relating the total and peak number of infections in two countries to the rate of travel between them and their respective epidemiological parameters.

From the conclusions:

One interesting conclusion from our models is that typical international mobility – the probability per unit time of international travel for a given infected individual, estimated at mi→j ∼ 10−5 per week – is still sufficiently small that a country with well-developed public health infrastructure (effectively, a negative eigenvalue λ) can resist an epidemic even when other more populous countries experience complete saturation. In the quasi-realistic simulation 1 (figures (1),(2)), of order 10^5 infections occur in country 2, even though the disease has swept completely through country 1. In reaching this conclusion, we kept the mobility parameter fixed during the outbreak, and did not assume any draconian quarantine on international travelers arriving in country 2. Such measures would reduce the number of infections in country 2 considerably. Of course, this conclusion assumes that the public health infrastructure in country 2 remains robust during the outbreak. In the nonlinear simulation 3 (figures (6), (7)), we see that a breakdown in the medical system can lead to grave consequences.